Designing of six sigma-based variable acceptance sampling plans where sample size is a critical choice

In variable sampling plans (VSPs), once a lot is submitted for inspection, the decision to accept/reject the lot is made after checking the quality of a measurable critical-to-quality (CTQ) characteristic against its specification. Under the assumption of normality with known standard deviation, we determine the quality level of the lot such as Six Sigma, Five Sigma, Four Sigma and Three Sigma relating to the VSP. With a specified sample size, the estimated parameter values are then used to determine the acceptable quality level (AQL) and the limiting quality level (LQL) that satisfy both the producer’s and consumer’s risks simultaneously. We have done extensive computations in our numerical evaluations to develop the operating characteristic (OC) curves for obtaining the recommended AQL and LQL values. Unlike existing methods, our approach helps to determine appropriate AQL and LQL values in tune with the quality level of the lot so as to achieve the required probabilities of acceptance of the lot, particularly, when inspection is based on destructive tests where the choice of sample size is critical. We have developed codes for computations using MATLAB R2020b. Illustrative examples are given to showcase the working of the proposed method.